Cytokines in the interleukin (IL)-23/IL-17 axis are central to psoriasis pathogenesis. Janus kinase (JAK) signal transducer and activator of transcription (STAT) regulates intracellular signalling of several cytokines (including IL-12, 23, 22, 6, 17, and interferon (IFN)-γ) in the IL-23/IL-17 axis, and, as a result, has become a therapeutic target for psoriasis treatment. Although several JAK1-3 inhibitors, with varying degrees of selectivity, have been developed for immune-mediated inflammatory diseases, use in psoriasis is limited by a low therapeutic index as anticipated by signals from other disease indications. More selective inhibition of the JAK family is an area of interest. Specifically, selective tyrosine kinase (TYK)2 inhibition suppresses IL-23/IL-17 axis signalling, and at therapeutic doses, has a favorable safety profile compared to therapeutic doses of JAK1-3 inhibitors. Phase III efficacy and safety data for the selective allosteric TYK2-inhibitor, deucravacitinib, in adult patients with moderate-to-severe plaque psoriasis is promising. Furthermore, phase II clinical trials for ropsacitinib (PF-06826647), a selective TYK2 inhibitor, and brepocitinib (PF-06700841), a JAK1/TYK2 inhibitor, have also demonstrated efficacy and an acceptable safety profile in adult patients with moderate-to-severe plaque psoriasis. Other novel TYK2 allosteric inhibitors, NDI-034858 and ESK-001, are currently being investigated in adult patients with plaque psoriasis. This article reviews the details of the JAK-STAT pathway in psoriasis pathophysiology, the rationale for selective targeting of JAKs in the treatment of psoriasis, and provides clinical perspective on clinical trial data for JAK and TYK2 inhibitors.